Even when bought packaged from the supermarket, fish fillets most often come with their skins on - which helps them to maintain their shape. The technique of skinning a fish fillet is important; if the skin and the flesh are not separated properly, the flesh may come away with the skin or he ragged and torn.
Lay the fillet skin-side down and make a cut across the flesh at the tail end. Dip your fingertips in salt to help you get a good grip, grasp the tail end and insert the knife in the cut. Working away from you and using a sawing action, hold the knife at a shallow angle. Move the knife between the flesh and skin until you reach the other end of the fillet.